Scholarlink

<p>Motivated by the discrete-time Toda (HADT) equation and quotient-quotient-difference (QQD) scheme together with their hungry forms (hHADT equation and hQQD scheme), we derive a new class of discrete integrable systems by considering the determinant structures of bivariate orthogonal polynomials associated with the genus-two hyper-elliptic curves. The corresponding Lax pairs are expressed through the recurrence relations of this class of bivariate orthogonal polynomials. Our study emphasizes the richer structures of genus-two hyper-elliptic curves, in contrast to the genus-one curve considered in the HADT and QQD cases, as well as in the hHADT and hQQD cases.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Novel Discrete Integrable System Related to Hyper-Elliptic Curves of Genus Two

  • 期刊论文

  • 发表日期：

    2025年2月25日

查看全文
  • Jing-Rui Wu,
  • Xing-Biao Hu

摘要

Motivated by the discrete-time Toda (HADT) equation and quotient-quotient-difference (QQD) scheme together with their hungry forms (hHADT equation and hQQD scheme), we derive a new class of discrete integrable systems by considering the determinant structures of bivariate orthogonal polynomials associated with the genus-two hyper-elliptic curves. The corresponding Lax pairs are expressed through the recurrence relations of this class of bivariate orthogonal polynomials. Our study emphasizes the richer structures of genus-two hyper-elliptic curves, in contrast to the genus-one curve considered in the HADT and QQD cases, as well as in the hHADT and hQQD cases.